If I make a purchase with my credit card there is a delay of a few days before it shows up on my online statement.
If I make a purchase with my debit card it usually is displayed that day.
Why the delay with a credit card statement?
It all depends on the merchant. When you charge your card the information goes through but it waits for the merchant to send the info/confirm the charge before it shows up on your online activity.
For example: I use Intuit to accept CC payments. When I charge an Amex the info is sent to Amex on the spot which is why your credit limit updates immediately but Amex then waits for a confirmation. Intuit actually handles the entire process which is probably how all CC processing services work.
When you use your debit card in a debit transaction you are withdrawing cash from your checking account, which is in part why debit transactions do not have the same security as credit.
Another note about debit cards and referring to mhoran_psprep comment -
I believe a delay is the result of the time it takes for all the information to change hands from when the transaction is created to when it is posted to your account.
The delay could be longer or shorter depending on how many transactions are being processed or perhaps how many transactions are being submitted. The amount of time would also then have to depend on your bank since it is their software posting these transactions. Also if you do a transaction on a Friday or before a holiday it probably won't post till after the weekend or holiday.